Question

The time after which they are closest to each other

• A. $1/3s$
• B. $8/3s$
• C. $1/5s$
• D. $8/5s$

Answer 1

Answer: (D)

$8/5s$

Taking $N$ as $+y-axis$ and $E$ as $+xAxis$
Imagine yourself as an observer sitting inside the car. You will regard the car as being at rest (at $C$). Relative to you, the speed of the motorcyclist is obtained by imposing the reversed velocity of the car on motorcyclist as shown in Fig. $v_m=15m{s}^{-1},v_c=20m{s}^{-1}$
$v_{mC}=\sqrt{{15}^2+{20}^2}=25m{s}^{-1}$
$\theta ={\tan }^{-1}\left(\frac{20}{15}\right)={53}^{\circ }$ with x-axis
The motorcyclist appears to move along the line $MP$ with speed $25m{s}^{-1}$.
The shortest distance $=$ perpendicular distance of $MP$ from $C=d\Rightarrow d=50\cos {53}^{\circ }\Rightarrow d=30m$
Time taken to come closed $=$ time taken by motorcyclist to reach $B$
$t=\frac{MB}{v_{mc}}=\frac{50\sin {53}^{\circ }}{25}\Rightarrow t=1.6s$.